TSTP Solution File: GEO201+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:37 EDT 2022
% Result : Theorem 11.92s 3.45s
% Output : Proof 24.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 17:01:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.54/0.61 ____ _
% 0.54/0.61 ___ / __ \_____(_)___ ________ __________
% 0.54/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.61
% 0.54/0.61 A Theorem Prover for First-Order Logic
% 0.54/0.61 (ePrincess v.1.0)
% 0.54/0.61
% 0.54/0.61 (c) Philipp Rümmer, 2009-2015
% 0.54/0.61 (c) Peter Backeman, 2014-2015
% 0.54/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.61 Bug reports to peter@backeman.se
% 0.54/0.61
% 0.54/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.61
% 0.54/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.71/0.96 Prover 0: Preprocessing ...
% 2.00/1.09 Prover 0: Warning: ignoring some quantifiers
% 2.00/1.11 Prover 0: Constructing countermodel ...
% 2.75/1.34 Prover 0: gave up
% 2.75/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.75/1.36 Prover 1: Preprocessing ...
% 2.96/1.44 Prover 1: Constructing countermodel ...
% 3.31/1.47 Prover 1: gave up
% 3.31/1.47 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.43/1.49 Prover 2: Preprocessing ...
% 3.66/1.60 Prover 2: Warning: ignoring some quantifiers
% 3.66/1.61 Prover 2: Constructing countermodel ...
% 4.32/1.69 Prover 2: gave up
% 4.32/1.69 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.32/1.71 Prover 3: Preprocessing ...
% 4.32/1.72 Prover 3: Warning: ignoring some quantifiers
% 4.32/1.72 Prover 3: Constructing countermodel ...
% 4.75/1.79 Prover 3: gave up
% 4.75/1.79 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 4.80/1.80 Prover 4: Preprocessing ...
% 4.94/1.88 Prover 4: Warning: ignoring some quantifiers
% 4.94/1.88 Prover 4: Constructing countermodel ...
% 9.72/3.01 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 9.72/3.02 Prover 5: Preprocessing ...
% 10.13/3.07 Prover 5: Constructing countermodel ...
% 11.92/3.45 Prover 5: proved (434ms)
% 11.92/3.45 Prover 4: stopped
% 11.92/3.45
% 11.92/3.45 No countermodel exists, formula is valid
% 11.92/3.45 % SZS status Theorem for theBenchmark
% 11.92/3.45
% 11.92/3.45 Generating proof ... found it (size 467)
% 23.56/6.23
% 23.56/6.23 % SZS output start Proof for theBenchmark
% 23.56/6.24 Assumed formulas after preprocessing and simplification:
% 23.56/6.24 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v1) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (intersection_point(v1, v0) = v3 & intersection_point(v0, v1) = v2 & convergent_lines(v0, v1) = 0 & distinct_points(v2, v3) = 0)
% 23.56/6.29 | Applying alpha-rule on (0) yields:
% 23.56/6.29 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 23.56/6.29 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 23.56/6.30 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0)))))
% 23.56/6.30 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 23.56/6.30 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 23.56/6.30 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 23.56/6.30 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 23.56/6.30 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 23.56/6.30 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.56/6.30 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 23.56/6.30 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 23.56/6.30 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 23.56/6.30 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 23.56/6.30 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 23.93/6.30 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0)))
% 23.93/6.30 | (16) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 23.93/6.30 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 23.93/6.31 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 23.93/6.31 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 23.93/6.31 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 23.93/6.31 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 23.93/6.31 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v1) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 23.93/6.31 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 23.93/6.31 | (24) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (intersection_point(v1, v0) = v3 & intersection_point(v0, v1) = v2 & convergent_lines(v0, v1) = 0 & distinct_points(v2, v3) = 0)
% 23.93/6.31 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.93/6.31 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 23.93/6.31 | (27) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 23.93/6.31 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 23.93/6.31 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 23.93/6.31 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 23.93/6.31 | (31) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 23.93/6.31 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0)))))
% 23.93/6.31 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 23.93/6.31 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 23.93/6.31 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 23.93/6.32 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 23.93/6.32 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0))
% 23.93/6.32 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 23.93/6.32 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 23.93/6.32 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 23.93/6.32 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 23.93/6.32 | (42) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 23.93/6.32 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 23.93/6.32 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 23.93/6.32 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0)))))
% 23.93/6.32 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 23.93/6.32 |
% 23.93/6.32 | Instantiating (24) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3 yields:
% 23.93/6.32 | (47) intersection_point(all_1_2_2, all_1_3_3) = all_1_0_0 & intersection_point(all_1_3_3, all_1_2_2) = all_1_1_1 & convergent_lines(all_1_3_3, all_1_2_2) = 0 & distinct_points(all_1_1_1, all_1_0_0) = 0
% 23.93/6.32 |
% 23.93/6.32 | Applying alpha-rule on (47) yields:
% 23.93/6.32 | (48) intersection_point(all_1_2_2, all_1_3_3) = all_1_0_0
% 23.93/6.32 | (49) intersection_point(all_1_3_3, all_1_2_2) = all_1_1_1
% 23.93/6.32 | (50) convergent_lines(all_1_3_3, all_1_2_2) = 0
% 23.93/6.32 | (51) distinct_points(all_1_1_1, all_1_0_0) = 0
% 23.93/6.32 |
% 23.93/6.32 | Instantiating formula (31) with all_1_3_3 yields:
% 23.93/6.32 | (52) ~ (convergent_lines(all_1_3_3, all_1_3_3) = 0)
% 23.93/6.32 |
% 23.93/6.32 | Instantiating formula (27) with all_1_1_1 yields:
% 23.93/6.32 | (53) ~ (distinct_points(all_1_1_1, all_1_1_1) = 0)
% 23.93/6.32 |
% 23.93/6.32 | Instantiating formula (42) with all_1_2_2, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_2_2) = 0, yields:
% 23.93/6.32 | (54) distinct_lines(all_1_3_3, all_1_2_2) = 0
% 23.93/6.32 |
% 23.93/6.32 | Instantiating formula (22) with 0, all_1_1_1, all_1_0_0, all_1_1_1 and discharging atoms distinct_points(all_1_1_1, all_1_0_0) = 0, yields:
% 23.93/6.32 | (55) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_1_1, all_1_0_0) = v0 & apart_point_and_line(all_1_1_1, v0) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.93/6.32 |
% 23.93/6.32 | Instantiating (55) with all_17_0_4, all_17_1_5, all_17_2_6 yields:
% 23.93/6.32 | (56) line_connecting(all_1_1_1, all_1_0_0) = all_17_2_6 & apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5 & distinct_points(all_1_1_1, all_1_1_1) = all_17_0_4 & ( ~ (all_17_1_5 = 0) | all_17_0_4 = 0)
% 23.93/6.32 |
% 23.93/6.32 | Applying alpha-rule on (56) yields:
% 23.93/6.32 | (57) line_connecting(all_1_1_1, all_1_0_0) = all_17_2_6
% 23.93/6.32 | (58) apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5
% 23.93/6.32 | (59) distinct_points(all_1_1_1, all_1_1_1) = all_17_0_4
% 23.93/6.32 | (60) ~ (all_17_1_5 = 0) | all_17_0_4 = 0
% 23.93/6.33 |
% 23.93/6.33 | Using (59) and (53) yields:
% 23.93/6.33 | (61) ~ (all_17_0_4 = 0)
% 23.93/6.33 |
% 23.93/6.33 +-Applying beta-rule and splitting (60), into two cases.
% 23.93/6.33 |-Branch one:
% 23.93/6.33 | (62) ~ (all_17_1_5 = 0)
% 23.93/6.33 |
% 23.93/6.33 | Instantiating formula (44) with all_17_1_5, all_17_1_5, all_17_2_6, all_17_2_6, all_1_0_0, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, distinct_points(all_1_1_1, all_1_0_0) = 0, yields:
% 23.93/6.33 | (63) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & distinct_lines(all_17_2_6, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.33 |
% 23.93/6.33 | Instantiating formula (21) with all_17_1_5, all_17_1_5, all_17_2_6, all_17_2_6, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, yields:
% 23.93/6.33 | (64) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & distinct_lines(all_17_2_6, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.33 |
% 23.93/6.33 | Instantiating formula (43) with all_1_2_2, all_1_3_3, all_1_0_0, all_1_1_1 and discharging atoms distinct_lines(all_1_3_3, all_1_2_2) = 0, distinct_points(all_1_1_1, all_1_0_0) = 0, yields:
% 23.93/6.33 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v3 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v1 & apart_point_and_line(all_1_1_1, all_1_3_3) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 23.93/6.33 |
% 23.93/6.33 | Instantiating formula (46) with all_17_0_4, all_1_1_1, all_1_0_0, all_1_1_1 and discharging atoms distinct_points(all_1_1_1, all_1_0_0) = 0, distinct_points(all_1_1_1, all_1_1_1) = all_17_0_4, yields:
% 23.93/6.33 | (66) all_17_0_4 = 0 | distinct_points(all_1_0_0, all_1_1_1) = 0
% 23.93/6.33 |
% 23.93/6.33 | Instantiating formula (37) with all_17_0_4, 0, all_1_1_1, all_1_1_1, all_1_0_0 and discharging atoms distinct_points(all_1_1_1, all_1_0_0) = 0, distinct_points(all_1_1_1, all_1_1_1) = all_17_0_4, yields:
% 23.93/6.33 | (67) all_17_0_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_0_0, all_1_1_1) = v1 & apart_point_and_line(all_1_1_1, v1) = v2 & distinct_points(all_1_0_0, all_1_1_1) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.93/6.33 |
% 23.93/6.33 | Instantiating formula (3) with all_17_0_4, all_1_1_1, all_1_1_1, all_1_2_2, all_1_3_3 and discharging atoms intersection_point(all_1_3_3, all_1_2_2) = all_1_1_1, distinct_points(all_1_1_1, all_1_1_1) = all_17_0_4, yields:
% 23.93/6.33 | (68) all_17_0_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & convergent_lines(all_1_3_3, all_1_2_2) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0))))
% 23.93/6.33 |
% 23.93/6.33 | Instantiating (65) with all_32_0_7, all_32_1_8, all_32_2_9, all_32_3_10 yields:
% 23.93/6.33 | (69) apart_point_and_line(all_1_0_0, all_1_2_2) = all_32_0_7 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_32_1_8 & apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9 & apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10 & (all_32_0_7 = 0 | all_32_1_8 = 0 | all_32_2_9 = 0 | all_32_3_10 = 0)
% 23.93/6.33 |
% 23.93/6.33 | Applying alpha-rule on (69) yields:
% 23.93/6.33 | (70) apart_point_and_line(all_1_0_0, all_1_3_3) = all_32_1_8
% 23.93/6.33 | (71) apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10
% 23.93/6.33 | (72) apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9
% 23.93/6.33 | (73) all_32_0_7 = 0 | all_32_1_8 = 0 | all_32_2_9 = 0 | all_32_3_10 = 0
% 23.93/6.33 | (74) apart_point_and_line(all_1_0_0, all_1_2_2) = all_32_0_7
% 23.93/6.33 |
% 23.93/6.33 +-Applying beta-rule and splitting (66), into two cases.
% 23.93/6.33 |-Branch one:
% 23.93/6.33 | (75) distinct_points(all_1_0_0, all_1_1_1) = 0
% 23.93/6.33 |
% 23.93/6.33 +-Applying beta-rule and splitting (68), into two cases.
% 23.93/6.33 |-Branch one:
% 23.93/6.33 | (76) all_17_0_4 = 0
% 23.93/6.33 |
% 23.93/6.33 | Equations (76) can reduce 61 to:
% 23.93/6.33 | (77) $false
% 23.93/6.33 |
% 23.93/6.33 |-The branch is then unsatisfiable
% 23.93/6.33 |-Branch two:
% 23.93/6.33 | (61) ~ (all_17_0_4 = 0)
% 23.93/6.33 | (79) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & convergent_lines(all_1_3_3, all_1_2_2) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0))))
% 23.93/6.33 |
% 23.93/6.33 | Instantiating (79) with all_42_0_11, all_42_1_12, all_42_2_13 yields:
% 23.93/6.33 | (80) apart_point_and_line(all_1_1_1, all_1_2_2) = all_42_0_11 & apart_point_and_line(all_1_1_1, all_1_3_3) = all_42_1_12 & convergent_lines(all_1_3_3, all_1_2_2) = all_42_2_13 & ( ~ (all_42_2_13 = 0) | ( ~ (all_42_0_11 = 0) & ~ (all_42_1_12 = 0)))
% 23.93/6.33 |
% 23.93/6.33 | Applying alpha-rule on (80) yields:
% 23.93/6.33 | (81) apart_point_and_line(all_1_1_1, all_1_2_2) = all_42_0_11
% 23.93/6.33 | (82) apart_point_and_line(all_1_1_1, all_1_3_3) = all_42_1_12
% 23.93/6.33 | (83) convergent_lines(all_1_3_3, all_1_2_2) = all_42_2_13
% 23.93/6.33 | (84) ~ (all_42_2_13 = 0) | ( ~ (all_42_0_11 = 0) & ~ (all_42_1_12 = 0))
% 23.93/6.33 |
% 23.93/6.33 +-Applying beta-rule and splitting (67), into two cases.
% 23.93/6.33 |-Branch one:
% 23.93/6.33 | (76) all_17_0_4 = 0
% 23.93/6.33 |
% 23.93/6.33 | Equations (76) can reduce 61 to:
% 23.93/6.33 | (77) $false
% 23.93/6.33 |
% 23.93/6.33 |-The branch is then unsatisfiable
% 23.93/6.33 |-Branch two:
% 23.93/6.33 | (61) ~ (all_17_0_4 = 0)
% 23.93/6.33 | (88) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_0_0, all_1_1_1) = v1 & apart_point_and_line(all_1_1_1, v1) = v2 & distinct_points(all_1_0_0, all_1_1_1) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.93/6.33 |
% 23.93/6.33 | Instantiating (88) with all_47_0_14, all_47_1_15, all_47_2_16 yields:
% 23.93/6.33 | (89) line_connecting(all_1_0_0, all_1_1_1) = all_47_1_15 & apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14 & distinct_points(all_1_0_0, all_1_1_1) = all_47_2_16 & ( ~ (all_47_0_14 = 0) | ~ (all_47_2_16 = 0))
% 23.93/6.33 |
% 23.93/6.33 | Applying alpha-rule on (89) yields:
% 23.93/6.33 | (90) line_connecting(all_1_0_0, all_1_1_1) = all_47_1_15
% 23.93/6.34 | (91) apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14
% 23.93/6.34 | (92) distinct_points(all_1_0_0, all_1_1_1) = all_47_2_16
% 23.93/6.34 | (93) ~ (all_47_0_14 = 0) | ~ (all_47_2_16 = 0)
% 23.93/6.34 |
% 23.93/6.34 +-Applying beta-rule and splitting (63), into two cases.
% 23.93/6.34 |-Branch one:
% 23.93/6.34 | (94) all_17_1_5 = 0
% 23.93/6.34 |
% 23.93/6.34 | Equations (94) can reduce 62 to:
% 23.93/6.34 | (77) $false
% 23.93/6.34 |
% 23.93/6.34 |-The branch is then unsatisfiable
% 23.93/6.34 |-Branch two:
% 23.93/6.34 | (62) ~ (all_17_1_5 = 0)
% 23.93/6.34 | (97) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & distinct_lines(all_17_2_6, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.34 |
% 23.93/6.34 | Instantiating (97) with all_58_0_20, all_58_1_21, all_58_2_22 yields:
% 23.93/6.34 | (98) apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_0_20 & apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_1_21 & distinct_lines(all_17_2_6, all_17_2_6) = all_58_2_22 & ( ~ (all_58_2_22 = 0) | all_58_0_20 = 0 | all_58_1_21 = 0)
% 23.93/6.34 |
% 23.93/6.34 | Applying alpha-rule on (98) yields:
% 23.93/6.34 | (99) apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_0_20
% 23.93/6.34 | (100) apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_1_21
% 23.93/6.34 | (101) distinct_lines(all_17_2_6, all_17_2_6) = all_58_2_22
% 23.93/6.34 | (102) ~ (all_58_2_22 = 0) | all_58_0_20 = 0 | all_58_1_21 = 0
% 23.93/6.34 |
% 23.93/6.34 +-Applying beta-rule and splitting (64), into two cases.
% 23.93/6.34 |-Branch one:
% 23.93/6.34 | (94) all_17_1_5 = 0
% 23.93/6.34 |
% 23.93/6.34 | Equations (94) can reduce 62 to:
% 23.93/6.34 | (77) $false
% 23.93/6.34 |
% 23.93/6.34 |-The branch is then unsatisfiable
% 23.93/6.34 |-Branch two:
% 23.93/6.34 | (62) ~ (all_17_1_5 = 0)
% 23.93/6.34 | (106) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & distinct_lines(all_17_2_6, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.34 |
% 23.93/6.34 | Instantiating (106) with all_63_0_23, all_63_1_24, all_63_2_25, all_63_3_26 yields:
% 23.93/6.34 | (107) apart_point_and_line(all_1_1_1, all_17_2_6) = all_63_0_23 & apart_point_and_line(all_1_1_1, all_17_2_6) = all_63_1_24 & distinct_lines(all_17_2_6, all_17_2_6) = all_63_2_25 & distinct_points(all_1_1_1, all_1_1_1) = all_63_3_26 & ( ~ (all_63_2_25 = 0) | ~ (all_63_3_26 = 0) | all_63_0_23 = 0 | all_63_1_24 = 0)
% 23.93/6.34 |
% 23.93/6.34 | Applying alpha-rule on (107) yields:
% 23.93/6.34 | (108) apart_point_and_line(all_1_1_1, all_17_2_6) = all_63_0_23
% 23.93/6.34 | (109) ~ (all_63_2_25 = 0) | ~ (all_63_3_26 = 0) | all_63_0_23 = 0 | all_63_1_24 = 0
% 23.93/6.34 | (110) distinct_points(all_1_1_1, all_1_1_1) = all_63_3_26
% 23.93/6.34 | (111) distinct_lines(all_17_2_6, all_17_2_6) = all_63_2_25
% 23.93/6.34 | (112) apart_point_and_line(all_1_1_1, all_17_2_6) = all_63_1_24
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_58_1_21, all_58_0_20 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_0_20, apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_1_21, yields:
% 23.93/6.34 | (113) all_58_0_20 = all_58_1_21
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (14) with all_1_1_1, all_17_2_6, all_63_0_23, all_17_1_5 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_63_0_23, apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, yields:
% 23.93/6.34 | (114) all_63_0_23 = all_17_1_5
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (14) with all_1_1_1, all_17_2_6, all_63_1_24, all_63_0_23 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_63_0_23, apart_point_and_line(all_1_1_1, all_17_2_6) = all_63_1_24, yields:
% 23.93/6.34 | (115) all_63_0_23 = all_63_1_24
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (14) with all_1_1_1, all_1_2_2, all_32_2_9, all_42_0_11 and discharging atoms apart_point_and_line(all_1_1_1, all_1_2_2) = all_42_0_11, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.34 | (116) all_42_0_11 = all_32_2_9
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (14) with all_1_1_1, all_1_3_3, all_32_3_10, all_42_1_12 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_42_1_12, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.34 | (117) all_42_1_12 = all_32_3_10
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (11) with all_1_3_3, all_1_2_2, all_42_2_13, 0 and discharging atoms convergent_lines(all_1_3_3, all_1_2_2) = all_42_2_13, convergent_lines(all_1_3_3, all_1_2_2) = 0, yields:
% 23.93/6.34 | (118) all_42_2_13 = 0
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (5) with all_1_0_0, all_1_1_1, 0, all_47_2_16 and discharging atoms distinct_points(all_1_0_0, all_1_1_1) = all_47_2_16, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.34 | (119) all_47_2_16 = 0
% 23.93/6.34 |
% 23.93/6.34 | Combining equations (114,115) yields a new equation:
% 23.93/6.34 | (120) all_63_1_24 = all_17_1_5
% 23.93/6.34 |
% 23.93/6.34 | From (113) and (99) follows:
% 23.93/6.34 | (100) apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_1_21
% 23.93/6.34 |
% 23.93/6.34 | From (120) and (112) follows:
% 23.93/6.34 | (58) apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5
% 23.93/6.34 |
% 23.93/6.34 | From (116) and (81) follows:
% 23.93/6.34 | (72) apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9
% 23.93/6.34 |
% 23.93/6.34 | From (117) and (82) follows:
% 23.93/6.34 | (71) apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10
% 23.93/6.34 |
% 23.93/6.34 | From (118) and (83) follows:
% 23.93/6.34 | (50) convergent_lines(all_1_3_3, all_1_2_2) = 0
% 23.93/6.34 |
% 23.93/6.34 | From (119) and (92) follows:
% 23.93/6.34 | (75) distinct_points(all_1_0_0, all_1_1_1) = 0
% 23.93/6.34 |
% 23.93/6.34 +-Applying beta-rule and splitting (84), into two cases.
% 23.93/6.34 |-Branch one:
% 23.93/6.34 | (127) ~ (all_42_2_13 = 0)
% 23.93/6.34 |
% 23.93/6.34 | Equations (118) can reduce 127 to:
% 23.93/6.34 | (77) $false
% 23.93/6.34 |
% 23.93/6.34 |-The branch is then unsatisfiable
% 23.93/6.34 |-Branch two:
% 23.93/6.34 | (118) all_42_2_13 = 0
% 23.93/6.34 | (130) ~ (all_42_0_11 = 0) & ~ (all_42_1_12 = 0)
% 23.93/6.34 |
% 23.93/6.34 | Applying alpha-rule on (130) yields:
% 23.93/6.34 | (131) ~ (all_42_0_11 = 0)
% 23.93/6.34 | (132) ~ (all_42_1_12 = 0)
% 23.93/6.34 |
% 23.93/6.34 | Equations (116) can reduce 131 to:
% 23.93/6.34 | (133) ~ (all_32_2_9 = 0)
% 23.93/6.34 |
% 23.93/6.34 | Equations (117) can reduce 132 to:
% 23.93/6.34 | (134) ~ (all_32_3_10 = 0)
% 23.93/6.34 |
% 23.93/6.34 +-Applying beta-rule and splitting (93), into two cases.
% 23.93/6.34 |-Branch one:
% 23.93/6.34 | (135) ~ (all_47_0_14 = 0)
% 23.93/6.34 |
% 23.93/6.34 | Instantiating formula (45) with all_1_0_0, all_32_0_7, all_1_0_0, all_1_3_3, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_0_0, all_1_2_2) = all_32_0_7, yields:
% 23.93/6.35 | (136) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & convergent_lines(all_1_2_2, all_1_3_3) = v0 & distinct_points(all_1_0_0, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_32_0_7 = 0))))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (32) with all_1_0_0, all_32_1_8, all_1_0_0, all_1_3_3, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_0_0, all_1_3_3) = all_32_1_8, yields:
% 23.93/6.35 | (137) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_3_3) = v0 & distinct_points(all_1_0_0, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_32_1_8 = 0))))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (21) with all_47_0_14, all_17_1_5, all_47_1_15, all_17_2_6, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, yields:
% 23.93/6.35 | (138) all_47_0_14 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & distinct_lines(all_17_2_6, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (21) with all_17_1_5, all_47_0_14, all_17_2_6, all_47_1_15, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, yields:
% 23.93/6.35 | (139) all_47_0_14 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & distinct_lines(all_47_1_15, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (4) with all_47_0_14, all_17_1_5, all_17_2_6, all_47_1_15, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, yields:
% 23.93/6.35 | (140) all_47_0_14 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & distinct_lines(all_47_1_15, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (4) with all_17_1_5, all_47_0_14, all_47_1_15, all_17_2_6, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, yields:
% 23.93/6.35 | (141) all_47_0_14 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & distinct_lines(all_17_2_6, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (4) with all_47_0_14, all_58_1_21, all_17_2_6, all_47_1_15, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_1_21, apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, yields:
% 23.93/6.35 | (142) all_58_1_21 = 0 | all_47_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & distinct_lines(all_47_1_15, all_17_2_6) = v1 & distinct_points(all_1_0_0, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (21) with all_32_1_8, all_47_0_14, all_1_3_3, all_47_1_15, all_1_0_0, all_1_1_1 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_32_1_8, apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, yields:
% 23.93/6.35 | (143) all_47_0_14 = 0 | all_32_1_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (21) with all_47_0_14, all_47_0_14, all_47_1_15, all_47_1_15, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, yields:
% 23.93/6.35 | (144) all_47_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & distinct_lines(all_47_1_15, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (21) with all_32_2_9, all_17_1_5, all_1_2_2, all_17_2_6, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.35 | (145) all_32_2_9 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_17_2_6, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (21) with all_17_1_5, all_32_2_9, all_17_2_6, all_1_2_2, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.35 | (146) all_32_2_9 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (4) with all_32_2_9, all_17_1_5, all_17_2_6, all_1_2_2, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.35 | (147) all_32_2_9 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.35 |
% 23.93/6.35 | Instantiating formula (4) with all_17_1_5, all_32_2_9, all_1_2_2, all_17_2_6, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.35 | (148) all_32_2_9 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_17_2_6, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_32_2_9, all_47_0_14, all_1_2_2, all_47_1_15, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.36 | (149) all_47_0_14 = 0 | all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_47_1_15, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_47_0_14, all_32_2_9, all_47_1_15, all_1_2_2, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.36 | (150) all_47_0_14 = 0 | all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (4) with all_32_2_9, all_47_0_14, all_47_1_15, all_1_2_2, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.36 | (151) all_47_0_14 = 0 | all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (4) with all_47_0_14, all_32_2_9, all_1_2_2, all_47_1_15, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.36 | (152) all_47_0_14 = 0 | all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_47_1_15, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_32_2_9, all_32_2_9, all_1_2_2, all_1_2_2, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.36 | (153) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (45) with all_1_0_0, all_32_2_9, all_1_1_1, all_1_3_3, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, yields:
% 23.93/6.36 | (154) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & convergent_lines(all_1_2_2, all_1_3_3) = v0 & distinct_points(all_1_1_1, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_32_2_9 = 0))))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_32_3_10, all_17_1_5, all_1_3_3, all_17_2_6, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (155) all_32_3_10 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_17_2_6, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_17_1_5, all_32_3_10, all_17_2_6, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (156) all_32_3_10 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (4) with all_32_3_10, all_17_1_5, all_17_2_6, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (157) all_32_3_10 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (4) with all_17_1_5, all_32_3_10, all_1_3_3, all_17_2_6, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (158) all_32_3_10 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_17_2_6, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_32_3_10, all_47_0_14, all_1_3_3, all_47_1_15, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (159) all_47_0_14 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_47_0_14, all_32_3_10, all_47_1_15, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (160) all_47_0_14 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (4) with all_32_3_10, all_47_0_14, all_47_1_15, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (161) all_47_0_14 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (4) with all_47_0_14, all_32_3_10, all_1_3_3, all_47_1_15, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (162) all_47_0_14 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (21) with all_32_3_10, all_32_2_9, all_1_3_3, all_1_2_2, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (163) all_32_2_9 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_2_2, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.36 |
% 23.93/6.36 | Instantiating formula (4) with all_32_2_9, all_32_3_10, all_1_3_3, all_1_2_2, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.36 | (164) all_32_2_9 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_2_2, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (21) with all_32_3_10, all_32_3_10, all_1_3_3, all_1_3_3, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.37 | (165) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (32) with all_1_0_0, all_32_3_10, all_1_1_1, all_1_3_3, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_3_3) = all_1_0_0, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, yields:
% 23.93/6.37 | (166) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_3_3) = v0 & distinct_points(all_1_1_1, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_32_3_10 = 0))))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (13) with 0, all_1_0_0, all_1_0_0, all_1_1_1 and discharging atoms distinct_points(all_1_0_0, all_1_1_1) = 0, distinct_points(all_1_1_1, all_1_0_0) = 0, yields:
% 23.93/6.37 | (167) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_1_1, all_1_0_0) = v0 & apart_point_and_line(all_1_0_0, v0) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (22) with 0, all_1_0_0, all_1_1_1, all_1_0_0 and discharging atoms distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (168) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_0_0, all_1_1_1) = v0 & apart_point_and_line(all_1_0_0, v0) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (35) with 0, all_17_2_6, all_1_0_0, all_1_0_0, all_1_1_1 and discharging atoms line_connecting(all_1_1_1, all_1_0_0) = all_17_2_6, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (169) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v2 & distinct_points(all_1_1_1, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (36) with 0, all_47_1_15, all_1_0_0, all_1_1_1, all_1_0_0 and discharging atoms line_connecting(all_1_0_0, all_1_1_1) = all_47_1_15, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (170) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v2 & distinct_points(all_1_0_0, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_17_1_5, all_47_0_14, all_17_2_6, all_47_1_15, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (171) all_47_0_14 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & distinct_lines(all_47_1_15, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_17_1_5, all_32_2_9, all_17_2_6, all_1_2_2, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (172) all_32_2_9 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_17_1_5, all_32_3_10, all_17_2_6, all_1_3_3, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (173) all_32_3_10 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_47_0_14, all_17_1_5, all_47_1_15, all_17_2_6, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (174) all_47_0_14 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & distinct_lines(all_17_2_6, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_47_0_14, all_47_0_14, all_47_1_15, all_47_1_15, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (175) all_47_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & distinct_lines(all_47_1_15, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_47_0_14, all_32_2_9, all_47_1_15, all_1_2_2, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (176) all_47_0_14 = 0 | all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_47_0_14, all_32_3_10, all_47_1_15, all_1_3_3, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (177) all_47_0_14 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_32_2_9, all_17_1_5, all_1_2_2, all_17_2_6, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (178) all_32_2_9 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_17_2_6, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_32_2_9, all_47_0_14, all_1_2_2, all_47_1_15, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (179) all_47_0_14 = 0 | all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_47_1_15, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_32_2_9, all_32_2_9, all_1_2_2, all_1_2_2, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (180) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.93/6.37 |
% 23.93/6.37 | Instantiating formula (6) with all_32_3_10, all_17_1_5, all_1_3_3, all_17_2_6, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_17_2_6) = all_17_1_5, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 23.93/6.37 | (181) all_32_3_10 = 0 | all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_17_2_6, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.37 |
% 24.28/6.37 | Instantiating formula (6) with all_32_3_10, all_47_0_14, all_1_3_3, all_47_1_15, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_47_1_15) = all_47_0_14, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 24.28/6.37 | (182) all_47_0_14 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.37 |
% 24.28/6.37 | Instantiating formula (6) with all_32_3_10, all_32_2_9, all_1_3_3, all_1_2_2, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_1_2_2) = all_32_2_9, apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 24.28/6.37 | (183) all_32_2_9 = 0 | all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_2_2, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.37 |
% 24.28/6.37 | Instantiating formula (6) with all_32_3_10, all_32_3_10, all_1_3_3, all_1_3_3, all_1_1_1, all_1_0_0 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_32_3_10, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 24.28/6.37 | (184) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.37 |
% 24.28/6.37 | Instantiating formula (43) with all_1_2_2, all_1_3_3, all_1_1_1, all_1_0_0 and discharging atoms distinct_lines(all_1_3_3, all_1_2_2) = 0, distinct_points(all_1_0_0, all_1_1_1) = 0, yields:
% 24.28/6.37 | (185) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v0 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 24.28/6.37 |
% 24.28/6.37 | Instantiating (185) with all_86_0_27, all_86_1_28, all_86_2_29, all_86_3_30 yields:
% 24.28/6.37 | (186) apart_point_and_line(all_1_0_0, all_1_2_2) = all_86_2_29 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_86_3_30 & apart_point_and_line(all_1_1_1, all_1_2_2) = all_86_0_27 & apart_point_and_line(all_1_1_1, all_1_3_3) = all_86_1_28 & (all_86_0_27 = 0 | all_86_1_28 = 0 | all_86_2_29 = 0 | all_86_3_30 = 0)
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (186) yields:
% 24.28/6.38 | (187) apart_point_and_line(all_1_1_1, all_1_2_2) = all_86_0_27
% 24.28/6.38 | (188) all_86_0_27 = 0 | all_86_1_28 = 0 | all_86_2_29 = 0 | all_86_3_30 = 0
% 24.28/6.38 | (189) apart_point_and_line(all_1_1_1, all_1_3_3) = all_86_1_28
% 24.28/6.38 | (190) apart_point_and_line(all_1_0_0, all_1_2_2) = all_86_2_29
% 24.28/6.38 | (191) apart_point_and_line(all_1_0_0, all_1_3_3) = all_86_3_30
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (169) with all_88_0_31, all_88_1_32, all_88_2_33 yields:
% 24.28/6.38 | (192) apart_point_and_line(all_1_0_0, all_17_2_6) = all_88_1_32 & distinct_points(all_1_0_0, all_1_0_0) = all_88_0_31 & distinct_points(all_1_1_1, all_1_0_0) = all_88_2_33 & ( ~ (all_88_1_32 = 0) | ~ (all_88_2_33 = 0) | all_88_0_31 = 0)
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (192) yields:
% 24.28/6.38 | (193) apart_point_and_line(all_1_0_0, all_17_2_6) = all_88_1_32
% 24.28/6.38 | (194) distinct_points(all_1_0_0, all_1_0_0) = all_88_0_31
% 24.28/6.38 | (195) distinct_points(all_1_1_1, all_1_0_0) = all_88_2_33
% 24.28/6.38 | (196) ~ (all_88_1_32 = 0) | ~ (all_88_2_33 = 0) | all_88_0_31 = 0
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (168) with all_90_0_34, all_90_1_35, all_90_2_36 yields:
% 24.28/6.38 | (197) line_connecting(all_1_0_0, all_1_1_1) = all_90_2_36 & apart_point_and_line(all_1_0_0, all_90_2_36) = all_90_1_35 & distinct_points(all_1_0_0, all_1_0_0) = all_90_0_34 & ( ~ (all_90_1_35 = 0) | all_90_0_34 = 0)
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (197) yields:
% 24.28/6.38 | (198) line_connecting(all_1_0_0, all_1_1_1) = all_90_2_36
% 24.28/6.38 | (199) apart_point_and_line(all_1_0_0, all_90_2_36) = all_90_1_35
% 24.28/6.38 | (200) distinct_points(all_1_0_0, all_1_0_0) = all_90_0_34
% 24.28/6.38 | (201) ~ (all_90_1_35 = 0) | all_90_0_34 = 0
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (166) with all_92_0_37, all_92_1_38, all_92_2_39 yields:
% 24.28/6.38 | (202) apart_point_and_line(all_1_1_1, all_1_2_2) = all_92_1_38 & convergent_lines(all_1_2_2, all_1_3_3) = all_92_2_39 & distinct_points(all_1_1_1, all_1_0_0) = all_92_0_37 & ( ~ (all_92_2_39 = 0) | all_92_0_37 = 0 | ( ~ (all_92_1_38 = 0) & ~ (all_32_3_10 = 0)))
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (202) yields:
% 24.28/6.38 | (203) apart_point_and_line(all_1_1_1, all_1_2_2) = all_92_1_38
% 24.28/6.38 | (204) convergent_lines(all_1_2_2, all_1_3_3) = all_92_2_39
% 24.28/6.38 | (205) distinct_points(all_1_1_1, all_1_0_0) = all_92_0_37
% 24.28/6.38 | (206) ~ (all_92_2_39 = 0) | all_92_0_37 = 0 | ( ~ (all_92_1_38 = 0) & ~ (all_32_3_10 = 0))
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (167) with all_94_0_40, all_94_1_41, all_94_2_42 yields:
% 24.28/6.38 | (207) line_connecting(all_1_1_1, all_1_0_0) = all_94_2_42 & apart_point_and_line(all_1_0_0, all_94_2_42) = all_94_1_41 & distinct_points(all_1_0_0, all_1_0_0) = all_94_0_40 & ( ~ (all_94_1_41 = 0) | all_94_0_40 = 0)
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (207) yields:
% 24.28/6.38 | (208) line_connecting(all_1_1_1, all_1_0_0) = all_94_2_42
% 24.28/6.38 | (209) apart_point_and_line(all_1_0_0, all_94_2_42) = all_94_1_41
% 24.28/6.38 | (210) distinct_points(all_1_0_0, all_1_0_0) = all_94_0_40
% 24.28/6.38 | (211) ~ (all_94_1_41 = 0) | all_94_0_40 = 0
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (170) with all_98_0_46, all_98_1_47, all_98_2_48 yields:
% 24.28/6.38 | (212) apart_point_and_line(all_1_0_0, all_47_1_15) = all_98_1_47 & distinct_points(all_1_0_0, all_1_0_0) = all_98_0_46 & distinct_points(all_1_0_0, all_1_1_1) = all_98_2_48 & ( ~ (all_98_1_47 = 0) | ~ (all_98_2_48 = 0) | all_98_0_46 = 0)
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (212) yields:
% 24.28/6.38 | (213) apart_point_and_line(all_1_0_0, all_47_1_15) = all_98_1_47
% 24.28/6.38 | (214) distinct_points(all_1_0_0, all_1_0_0) = all_98_0_46
% 24.28/6.38 | (215) distinct_points(all_1_0_0, all_1_1_1) = all_98_2_48
% 24.28/6.38 | (216) ~ (all_98_1_47 = 0) | ~ (all_98_2_48 = 0) | all_98_0_46 = 0
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (137) with all_100_0_49, all_100_1_50, all_100_2_51 yields:
% 24.28/6.38 | (217) apart_point_and_line(all_1_0_0, all_1_2_2) = all_100_1_50 & convergent_lines(all_1_2_2, all_1_3_3) = all_100_2_51 & distinct_points(all_1_0_0, all_1_0_0) = all_100_0_49 & ( ~ (all_100_2_51 = 0) | all_100_0_49 = 0 | ( ~ (all_100_1_50 = 0) & ~ (all_32_1_8 = 0)))
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (217) yields:
% 24.28/6.38 | (218) apart_point_and_line(all_1_0_0, all_1_2_2) = all_100_1_50
% 24.28/6.38 | (219) convergent_lines(all_1_2_2, all_1_3_3) = all_100_2_51
% 24.28/6.38 | (220) distinct_points(all_1_0_0, all_1_0_0) = all_100_0_49
% 24.28/6.38 | (221) ~ (all_100_2_51 = 0) | all_100_0_49 = 0 | ( ~ (all_100_1_50 = 0) & ~ (all_32_1_8 = 0))
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (154) with all_102_0_52, all_102_1_53, all_102_2_54 yields:
% 24.28/6.38 | (222) apart_point_and_line(all_1_1_1, all_1_3_3) = all_102_1_53 & convergent_lines(all_1_2_2, all_1_3_3) = all_102_2_54 & distinct_points(all_1_1_1, all_1_0_0) = all_102_0_52 & ( ~ (all_102_2_54 = 0) | all_102_0_52 = 0 | ( ~ (all_102_1_53 = 0) & ~ (all_32_2_9 = 0)))
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (222) yields:
% 24.28/6.38 | (223) apart_point_and_line(all_1_1_1, all_1_3_3) = all_102_1_53
% 24.28/6.38 | (224) convergent_lines(all_1_2_2, all_1_3_3) = all_102_2_54
% 24.28/6.38 | (225) distinct_points(all_1_1_1, all_1_0_0) = all_102_0_52
% 24.28/6.38 | (226) ~ (all_102_2_54 = 0) | all_102_0_52 = 0 | ( ~ (all_102_1_53 = 0) & ~ (all_32_2_9 = 0))
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (136) with all_104_0_55, all_104_1_56, all_104_2_57 yields:
% 24.28/6.38 | (227) apart_point_and_line(all_1_0_0, all_1_3_3) = all_104_1_56 & convergent_lines(all_1_2_2, all_1_3_3) = all_104_2_57 & distinct_points(all_1_0_0, all_1_0_0) = all_104_0_55 & ( ~ (all_104_2_57 = 0) | all_104_0_55 = 0 | ( ~ (all_104_1_56 = 0) & ~ (all_32_0_7 = 0)))
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (227) yields:
% 24.28/6.38 | (228) apart_point_and_line(all_1_0_0, all_1_3_3) = all_104_1_56
% 24.28/6.38 | (229) convergent_lines(all_1_2_2, all_1_3_3) = all_104_2_57
% 24.28/6.38 | (230) distinct_points(all_1_0_0, all_1_0_0) = all_104_0_55
% 24.28/6.38 | (231) ~ (all_104_2_57 = 0) | all_104_0_55 = 0 | ( ~ (all_104_1_56 = 0) & ~ (all_32_0_7 = 0))
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (175), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (232) all_47_0_14 = 0
% 24.28/6.38 |
% 24.28/6.38 | Equations (232) can reduce 135 to:
% 24.28/6.38 | (77) $false
% 24.28/6.38 |
% 24.28/6.38 |-The branch is then unsatisfiable
% 24.28/6.38 |-Branch two:
% 24.28/6.38 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.38 | (235) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & distinct_lines(all_47_1_15, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (144), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (232) all_47_0_14 = 0
% 24.28/6.38 |
% 24.28/6.38 | Equations (232) can reduce 135 to:
% 24.28/6.38 | (77) $false
% 24.28/6.38 |
% 24.28/6.38 |-The branch is then unsatisfiable
% 24.28/6.38 |-Branch two:
% 24.28/6.38 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.38 | (239) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & distinct_lines(all_47_1_15, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (184), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (240) all_32_3_10 = 0
% 24.28/6.38 |
% 24.28/6.38 | Equations (240) can reduce 134 to:
% 24.28/6.38 | (77) $false
% 24.28/6.38 |
% 24.28/6.38 |-The branch is then unsatisfiable
% 24.28/6.38 |-Branch two:
% 24.28/6.38 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.38 | (243) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.38 |
% 24.28/6.38 | Instantiating (243) with all_120_0_65, all_120_1_66, all_120_2_67 yields:
% 24.28/6.38 | (244) apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_0_65 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_1_66 & distinct_lines(all_1_3_3, all_1_3_3) = all_120_2_67 & ( ~ (all_120_2_67 = 0) | all_120_0_65 = 0 | all_120_1_66 = 0)
% 24.28/6.38 |
% 24.28/6.38 | Applying alpha-rule on (244) yields:
% 24.28/6.38 | (245) apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_0_65
% 24.28/6.38 | (246) apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_1_66
% 24.28/6.38 | (247) distinct_lines(all_1_3_3, all_1_3_3) = all_120_2_67
% 24.28/6.38 | (248) ~ (all_120_2_67 = 0) | all_120_0_65 = 0 | all_120_1_66 = 0
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (165), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (240) all_32_3_10 = 0
% 24.28/6.38 |
% 24.28/6.38 | Equations (240) can reduce 134 to:
% 24.28/6.38 | (77) $false
% 24.28/6.38 |
% 24.28/6.38 |-The branch is then unsatisfiable
% 24.28/6.38 |-Branch two:
% 24.28/6.38 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.38 | (252) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (180), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (253) all_32_2_9 = 0
% 24.28/6.38 |
% 24.28/6.38 | Equations (253) can reduce 133 to:
% 24.28/6.38 | (77) $false
% 24.28/6.38 |
% 24.28/6.38 |-The branch is then unsatisfiable
% 24.28/6.38 |-Branch two:
% 24.28/6.38 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.38 | (256) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (153), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (253) all_32_2_9 = 0
% 24.28/6.38 |
% 24.28/6.38 | Equations (253) can reduce 133 to:
% 24.28/6.38 | (77) $false
% 24.28/6.38 |
% 24.28/6.38 |-The branch is then unsatisfiable
% 24.28/6.38 |-Branch two:
% 24.28/6.38 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.38 | (260) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (151), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (232) all_47_0_14 = 0
% 24.28/6.38 |
% 24.28/6.38 | Equations (232) can reduce 135 to:
% 24.28/6.38 | (77) $false
% 24.28/6.38 |
% 24.28/6.38 |-The branch is then unsatisfiable
% 24.28/6.38 |-Branch two:
% 24.28/6.38 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.38 | (264) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.38 |
% 24.28/6.38 +-Applying beta-rule and splitting (182), into two cases.
% 24.28/6.38 |-Branch one:
% 24.28/6.38 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (268) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (181), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (240) all_32_3_10 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (240) can reduce 134 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.39 | (272) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_17_2_6, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (159), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (276) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (160), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (280) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (161), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (284) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (178), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (253) all_32_2_9 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (253) can reduce 133 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.39 | (288) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_17_2_6, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (146), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (253) all_32_2_9 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (253) can reduce 133 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.39 | (292) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (172), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (253) all_32_2_9 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (253) can reduce 133 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.39 | (296) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (145), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (253) all_32_2_9 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (253) can reduce 133 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.39 | (300) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_17_2_6, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (147), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (253) all_32_2_9 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (253) can reduce 133 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.39 | (304) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (149), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (308) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_47_1_15, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (179), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (312) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_47_1_15, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (176), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (316) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (150), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (320) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (162), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (324) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (148), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (253) all_32_2_9 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (253) can reduce 133 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.39 | (328) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_17_2_6, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (174), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (332) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & distinct_lines(all_17_2_6, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (171), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (232) all_47_0_14 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (232) can reduce 135 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.39 | (336) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & distinct_lines(all_47_1_15, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.39 |
% 24.28/6.39 +-Applying beta-rule and splitting (173), into two cases.
% 24.28/6.39 |-Branch one:
% 24.28/6.39 | (240) all_32_3_10 = 0
% 24.28/6.39 |
% 24.28/6.39 | Equations (240) can reduce 134 to:
% 24.28/6.39 | (77) $false
% 24.28/6.39 |
% 24.28/6.39 |-The branch is then unsatisfiable
% 24.28/6.39 |-Branch two:
% 24.28/6.39 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.39 | (340) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (163), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (253) all_32_2_9 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (253) can reduce 133 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.40 | (344) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_2_2, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (183), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (253) all_32_2_9 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (253) can reduce 133 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.40 | (348) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_2_2, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (164), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (253) all_32_2_9 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (253) can reduce 133 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.40 | (352) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_2_2, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (152), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (232) all_47_0_14 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (232) can reduce 135 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.40 | (356) all_32_2_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_47_1_15, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (155), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (240) all_32_3_10 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (240) can reduce 134 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.40 | (360) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_17_2_6, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (138), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (232) all_47_0_14 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (232) can reduce 135 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.40 | (364) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & distinct_lines(all_17_2_6, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (139), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (232) all_47_0_14 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (232) can reduce 135 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.40 | (368) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & distinct_lines(all_47_1_15, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (140), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (232) all_47_0_14 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (232) can reduce 135 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.40 | (372) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & distinct_lines(all_47_1_15, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (141), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (232) all_47_0_14 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (232) can reduce 135 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.40 | (376) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & distinct_lines(all_17_2_6, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (156), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (240) all_32_3_10 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (240) can reduce 134 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.40 | (380) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (177), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (232) all_47_0_14 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (232) can reduce 135 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.40 | (384) all_32_3_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (157), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (240) all_32_3_10 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (240) can reduce 134 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.40 | (388) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (158), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (240) all_32_3_10 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (240) can reduce 134 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.40 | (392) all_17_1_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_17_2_6, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (264), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (253) all_32_2_9 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (253) can reduce 133 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.40 | (396) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (268), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (240) all_32_3_10 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (240) can reduce 134 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.40 | (400) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.40 |
% 24.28/6.40 | Instantiating (400) with all_250_0_84, all_250_1_85, all_250_2_86 yields:
% 24.28/6.40 | (401) apart_point_and_line(all_1_0_0, all_47_1_15) = all_250_1_85 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_250_0_84 & distinct_lines(all_47_1_15, all_1_3_3) = all_250_2_86 & ( ~ (all_250_2_86 = 0) | all_250_0_84 = 0 | all_250_1_85 = 0)
% 24.28/6.40 |
% 24.28/6.40 | Applying alpha-rule on (401) yields:
% 24.28/6.40 | (402) apart_point_and_line(all_1_0_0, all_47_1_15) = all_250_1_85
% 24.28/6.40 | (403) apart_point_and_line(all_1_0_0, all_1_3_3) = all_250_0_84
% 24.28/6.40 | (404) distinct_lines(all_47_1_15, all_1_3_3) = all_250_2_86
% 24.28/6.40 | (405) ~ (all_250_2_86 = 0) | all_250_0_84 = 0 | all_250_1_85 = 0
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (272), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (94) all_17_1_5 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (94) can reduce 62 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.40 | (409) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_17_2_6, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.40 |
% 24.28/6.40 | Instantiating (409) with all_255_0_87, all_255_1_88, all_255_2_89 yields:
% 24.28/6.40 | (410) apart_point_and_line(all_1_0_0, all_17_2_6) = all_255_1_88 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_255_0_87 & distinct_lines(all_17_2_6, all_1_3_3) = all_255_2_89 & ( ~ (all_255_2_89 = 0) | all_255_0_87 = 0 | all_255_1_88 = 0)
% 24.28/6.40 |
% 24.28/6.40 | Applying alpha-rule on (410) yields:
% 24.28/6.40 | (411) apart_point_and_line(all_1_0_0, all_17_2_6) = all_255_1_88
% 24.28/6.40 | (412) apart_point_and_line(all_1_0_0, all_1_3_3) = all_255_0_87
% 24.28/6.40 | (413) distinct_lines(all_17_2_6, all_1_3_3) = all_255_2_89
% 24.28/6.40 | (414) ~ (all_255_2_89 = 0) | all_255_0_87 = 0 | all_255_1_88 = 0
% 24.28/6.40 |
% 24.28/6.40 +-Applying beta-rule and splitting (276), into two cases.
% 24.28/6.40 |-Branch one:
% 24.28/6.40 | (240) all_32_3_10 = 0
% 24.28/6.40 |
% 24.28/6.40 | Equations (240) can reduce 134 to:
% 24.28/6.40 | (77) $false
% 24.28/6.40 |
% 24.28/6.40 |-The branch is then unsatisfiable
% 24.28/6.40 |-Branch two:
% 24.28/6.40 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.40 | (418) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (280), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (240) all_32_3_10 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (240) can reduce 134 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.41 | (422) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (284), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (240) all_32_3_10 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (240) can reduce 134 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.41 | (426) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (288), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (430) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_17_2_6, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.41 |
% 24.28/6.41 | Instantiating (430) with all_275_0_102, all_275_1_103, all_275_2_104 yields:
% 24.28/6.41 | (431) apart_point_and_line(all_1_0_0, all_17_2_6) = all_275_1_103 & apart_point_and_line(all_1_0_0, all_1_2_2) = all_275_0_102 & distinct_lines(all_17_2_6, all_1_2_2) = all_275_2_104 & ( ~ (all_275_2_104 = 0) | all_275_0_102 = 0 | all_275_1_103 = 0)
% 24.28/6.41 |
% 24.28/6.41 | Applying alpha-rule on (431) yields:
% 24.28/6.41 | (432) apart_point_and_line(all_1_0_0, all_17_2_6) = all_275_1_103
% 24.28/6.41 | (433) apart_point_and_line(all_1_0_0, all_1_2_2) = all_275_0_102
% 24.28/6.41 | (434) distinct_lines(all_17_2_6, all_1_2_2) = all_275_2_104
% 24.28/6.41 | (435) ~ (all_275_2_104 = 0) | all_275_0_102 = 0 | all_275_1_103 = 0
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (292), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (439) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (296), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (443) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.41 |
% 24.28/6.41 | Instantiating (443) with all_285_0_109, all_285_1_110, all_285_2_111 yields:
% 24.28/6.41 | (444) apart_point_and_line(all_1_0_0, all_17_2_6) = all_285_0_109 & apart_point_and_line(all_1_0_0, all_1_2_2) = all_285_1_110 & distinct_lines(all_1_2_2, all_17_2_6) = all_285_2_111 & ( ~ (all_285_2_111 = 0) | all_285_0_109 = 0 | all_285_1_110 = 0)
% 24.28/6.41 |
% 24.28/6.41 | Applying alpha-rule on (444) yields:
% 24.28/6.41 | (445) apart_point_and_line(all_1_0_0, all_17_2_6) = all_285_0_109
% 24.28/6.41 | (446) apart_point_and_line(all_1_0_0, all_1_2_2) = all_285_1_110
% 24.28/6.41 | (447) distinct_lines(all_1_2_2, all_17_2_6) = all_285_2_111
% 24.28/6.41 | (448) ~ (all_285_2_111 = 0) | all_285_0_109 = 0 | all_285_1_110 = 0
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (300), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (452) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_17_2_6, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (304), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (456) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_17_2_6) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (308), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (253) all_32_2_9 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (253) can reduce 133 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.41 | (460) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & distinct_lines(all_47_1_15, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (312), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (253) all_32_2_9 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (253) can reduce 133 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.41 | (464) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_47_1_15, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (316), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (253) all_32_2_9 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (253) can reduce 133 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.41 | (468) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (320), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (253) all_32_2_9 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (253) can reduce 133 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.41 | (472) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_47_1_15) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (324), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (240) all_32_3_10 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (240) can reduce 134 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.41 | (476) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (328), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (480) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_17_2_6) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_17_2_6, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (332), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (484) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_17_2_6) = v1 & distinct_lines(all_17_2_6, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.41 |
% 24.28/6.41 | Instantiating (484) with all_330_0_142, all_330_1_143, all_330_2_144 yields:
% 24.28/6.41 | (485) apart_point_and_line(all_1_0_0, all_47_1_15) = all_330_0_142 & apart_point_and_line(all_1_0_0, all_17_2_6) = all_330_1_143 & distinct_lines(all_17_2_6, all_47_1_15) = all_330_2_144 & ( ~ (all_330_2_144 = 0) | all_330_0_142 = 0 | all_330_1_143 = 0)
% 24.28/6.41 |
% 24.28/6.41 | Applying alpha-rule on (485) yields:
% 24.28/6.41 | (486) apart_point_and_line(all_1_0_0, all_47_1_15) = all_330_0_142
% 24.28/6.41 | (487) apart_point_and_line(all_1_0_0, all_17_2_6) = all_330_1_143
% 24.28/6.41 | (488) distinct_lines(all_17_2_6, all_47_1_15) = all_330_2_144
% 24.28/6.41 | (489) ~ (all_330_2_144 = 0) | all_330_0_142 = 0 | all_330_1_143 = 0
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (336), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (493) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v1 & apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & distinct_lines(all_47_1_15, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.41 |
% 24.28/6.41 | Instantiating (493) with all_335_0_145, all_335_1_146, all_335_2_147 yields:
% 24.28/6.41 | (494) apart_point_and_line(all_1_0_0, all_47_1_15) = all_335_1_146 & apart_point_and_line(all_1_0_0, all_17_2_6) = all_335_0_145 & distinct_lines(all_47_1_15, all_17_2_6) = all_335_2_147 & ( ~ (all_335_2_147 = 0) | all_335_0_145 = 0 | all_335_1_146 = 0)
% 24.28/6.41 |
% 24.28/6.41 | Applying alpha-rule on (494) yields:
% 24.28/6.41 | (495) apart_point_and_line(all_1_0_0, all_47_1_15) = all_335_1_146
% 24.28/6.41 | (496) apart_point_and_line(all_1_0_0, all_17_2_6) = all_335_0_145
% 24.28/6.41 | (497) distinct_lines(all_47_1_15, all_17_2_6) = all_335_2_147
% 24.28/6.41 | (498) ~ (all_335_2_147 = 0) | all_335_0_145 = 0 | all_335_1_146 = 0
% 24.28/6.41 |
% 24.28/6.41 +-Applying beta-rule and splitting (340), into two cases.
% 24.28/6.41 |-Branch one:
% 24.28/6.41 | (94) all_17_1_5 = 0
% 24.28/6.41 |
% 24.28/6.41 | Equations (94) can reduce 62 to:
% 24.28/6.41 | (77) $false
% 24.28/6.41 |
% 24.28/6.41 |-The branch is then unsatisfiable
% 24.28/6.41 |-Branch two:
% 24.28/6.41 | (62) ~ (all_17_1_5 = 0)
% 24.28/6.41 | (502) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_17_2_6) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_17_2_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.41 |
% 24.28/6.41 | Instantiating (502) with all_340_0_148, all_340_1_149, all_340_2_150 yields:
% 24.28/6.42 | (503) apart_point_and_line(all_1_0_0, all_17_2_6) = all_340_0_148 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_340_1_149 & distinct_lines(all_1_3_3, all_17_2_6) = all_340_2_150 & ( ~ (all_340_2_150 = 0) | all_340_0_148 = 0 | all_340_1_149 = 0)
% 24.28/6.42 |
% 24.28/6.42 | Applying alpha-rule on (503) yields:
% 24.28/6.42 | (504) apart_point_and_line(all_1_0_0, all_17_2_6) = all_340_0_148
% 24.28/6.42 | (505) apart_point_and_line(all_1_0_0, all_1_3_3) = all_340_1_149
% 24.28/6.42 | (506) distinct_lines(all_1_3_3, all_17_2_6) = all_340_2_150
% 24.28/6.42 | (507) ~ (all_340_2_150 = 0) | all_340_0_148 = 0 | all_340_1_149 = 0
% 24.28/6.42 |
% 24.28/6.42 +-Applying beta-rule and splitting (344), into two cases.
% 24.28/6.42 |-Branch one:
% 24.28/6.42 | (240) all_32_3_10 = 0
% 24.28/6.42 |
% 24.28/6.42 | Equations (240) can reduce 134 to:
% 24.28/6.42 | (77) $false
% 24.28/6.42 |
% 24.28/6.42 |-The branch is then unsatisfiable
% 24.28/6.42 |-Branch two:
% 24.28/6.42 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.42 | (511) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_2_2, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.42 |
% 24.28/6.42 +-Applying beta-rule and splitting (348), into two cases.
% 24.28/6.42 |-Branch one:
% 24.28/6.42 | (240) all_32_3_10 = 0
% 24.28/6.42 |
% 24.28/6.42 | Equations (240) can reduce 134 to:
% 24.28/6.42 | (77) $false
% 24.28/6.42 |
% 24.28/6.42 |-The branch is then unsatisfiable
% 24.28/6.42 |-Branch two:
% 24.28/6.42 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.42 | (515) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & apart_point_and_line(all_1_0_0, all_1_3_3) = v2 & distinct_lines(all_1_2_2, all_1_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.42 |
% 24.28/6.42 | Instantiating (515) with all_350_0_155, all_350_1_156, all_350_2_157 yields:
% 24.28/6.42 | (516) apart_point_and_line(all_1_0_0, all_1_2_2) = all_350_1_156 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_350_0_155 & distinct_lines(all_1_2_2, all_1_3_3) = all_350_2_157 & ( ~ (all_350_2_157 = 0) | all_350_0_155 = 0 | all_350_1_156 = 0)
% 24.28/6.42 |
% 24.28/6.42 | Applying alpha-rule on (516) yields:
% 24.28/6.42 | (517) apart_point_and_line(all_1_0_0, all_1_2_2) = all_350_1_156
% 24.28/6.42 | (518) apart_point_and_line(all_1_0_0, all_1_3_3) = all_350_0_155
% 24.28/6.42 | (519) distinct_lines(all_1_2_2, all_1_3_3) = all_350_2_157
% 24.28/6.42 | (520) ~ (all_350_2_157 = 0) | all_350_0_155 = 0 | all_350_1_156 = 0
% 24.28/6.42 |
% 24.28/6.42 +-Applying beta-rule and splitting (352), into two cases.
% 24.28/6.42 |-Branch one:
% 24.28/6.42 | (240) all_32_3_10 = 0
% 24.28/6.42 |
% 24.28/6.42 | Equations (240) can reduce 134 to:
% 24.28/6.42 | (77) $false
% 24.28/6.42 |
% 24.28/6.42 |-The branch is then unsatisfiable
% 24.28/6.42 |-Branch two:
% 24.28/6.42 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.42 | (524) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_2_2) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_2_2, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.42 |
% 24.28/6.42 +-Applying beta-rule and splitting (356), into two cases.
% 24.28/6.42 |-Branch one:
% 24.28/6.42 | (253) all_32_2_9 = 0
% 24.28/6.42 |
% 24.28/6.42 | Equations (253) can reduce 133 to:
% 24.28/6.42 | (77) $false
% 24.28/6.42 |
% 24.28/6.42 |-The branch is then unsatisfiable
% 24.28/6.42 |-Branch two:
% 24.28/6.42 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.42 | (528) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_1_2_2) = v3 & distinct_lines(all_47_1_15, all_1_2_2) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.42 |
% 24.28/6.42 +-Applying beta-rule and splitting (384), into two cases.
% 24.28/6.42 |-Branch one:
% 24.28/6.42 | (240) all_32_3_10 = 0
% 24.28/6.42 |
% 24.28/6.42 | Equations (240) can reduce 134 to:
% 24.28/6.42 | (77) $false
% 24.28/6.42 |
% 24.28/6.42 |-The branch is then unsatisfiable
% 24.28/6.42 |-Branch two:
% 24.28/6.42 | (134) ~ (all_32_3_10 = 0)
% 24.28/6.42 | (532) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_0_0, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_47_1_15) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 24.28/6.42 |
% 24.28/6.42 | Instantiating (532) with all_395_0_190, all_395_1_191, all_395_2_192 yields:
% 24.28/6.42 | (533) apart_point_and_line(all_1_0_0, all_47_1_15) = all_395_0_190 & apart_point_and_line(all_1_0_0, all_1_3_3) = all_395_1_191 & distinct_lines(all_1_3_3, all_47_1_15) = all_395_2_192 & ( ~ (all_395_2_192 = 0) | all_395_0_190 = 0 | all_395_1_191 = 0)
% 24.28/6.42 |
% 24.28/6.42 | Applying alpha-rule on (533) yields:
% 24.28/6.42 | (534) apart_point_and_line(all_1_0_0, all_47_1_15) = all_395_0_190
% 24.28/6.42 | (535) apart_point_and_line(all_1_0_0, all_1_3_3) = all_395_1_191
% 24.28/6.42 | (536) distinct_lines(all_1_3_3, all_47_1_15) = all_395_2_192
% 24.28/6.42 | (537) ~ (all_395_2_192 = 0) | all_395_0_190 = 0 | all_395_1_191 = 0
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_335_0_145, all_340_0_148 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_340_0_148, apart_point_and_line(all_1_0_0, all_17_2_6) = all_335_0_145, yields:
% 24.28/6.42 | (538) all_340_0_148 = all_335_0_145
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_330_1_143, all_58_1_21 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_330_1_143, apart_point_and_line(all_1_0_0, all_17_2_6) = all_58_1_21, yields:
% 24.28/6.42 | (539) all_330_1_143 = all_58_1_21
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_285_0_109, all_335_0_145 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_335_0_145, apart_point_and_line(all_1_0_0, all_17_2_6) = all_285_0_109, yields:
% 24.28/6.42 | (540) all_335_0_145 = all_285_0_109
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_285_0_109, all_330_1_143 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_330_1_143, apart_point_and_line(all_1_0_0, all_17_2_6) = all_285_0_109, yields:
% 24.28/6.42 | (541) all_330_1_143 = all_285_0_109
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_275_1_103, all_285_0_109 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_285_0_109, apart_point_and_line(all_1_0_0, all_17_2_6) = all_275_1_103, yields:
% 24.28/6.42 | (542) all_285_0_109 = all_275_1_103
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_255_1_88, all_340_0_148 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_340_0_148, apart_point_and_line(all_1_0_0, all_17_2_6) = all_255_1_88, yields:
% 24.28/6.42 | (543) all_340_0_148 = all_255_1_88
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_17_2_6, all_88_1_32, all_275_1_103 and discharging atoms apart_point_and_line(all_1_0_0, all_17_2_6) = all_275_1_103, apart_point_and_line(all_1_0_0, all_17_2_6) = all_88_1_32, yields:
% 24.28/6.42 | (544) all_275_1_103 = all_88_1_32
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_350_0_155, all_395_1_191 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_395_1_191, apart_point_and_line(all_1_0_0, all_1_3_3) = all_350_0_155, yields:
% 24.28/6.42 | (545) all_395_1_191 = all_350_0_155
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_340_1_149, all_350_0_155 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_350_0_155, apart_point_and_line(all_1_0_0, all_1_3_3) = all_340_1_149, yields:
% 24.28/6.42 | (546) all_350_0_155 = all_340_1_149
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_255_0_87, all_340_1_149 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_340_1_149, apart_point_and_line(all_1_0_0, all_1_3_3) = all_255_0_87, yields:
% 24.28/6.42 | (547) all_340_1_149 = all_255_0_87
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_250_0_84, all_255_0_87 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_255_0_87, apart_point_and_line(all_1_0_0, all_1_3_3) = all_250_0_84, yields:
% 24.28/6.42 | (548) all_255_0_87 = all_250_0_84
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_120_0_65, all_32_1_8 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_0_65, apart_point_and_line(all_1_0_0, all_1_3_3) = all_32_1_8, yields:
% 24.28/6.42 | (549) all_120_0_65 = all_32_1_8
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_120_0_65, all_250_0_84 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_250_0_84, apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_0_65, yields:
% 24.28/6.42 | (550) all_250_0_84 = all_120_0_65
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_120_1_66, all_395_1_191 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_395_1_191, apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_1_66, yields:
% 24.28/6.42 | (551) all_395_1_191 = all_120_1_66
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_104_1_56, all_120_0_65 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_120_0_65, apart_point_and_line(all_1_0_0, all_1_3_3) = all_104_1_56, yields:
% 24.28/6.42 | (552) all_120_0_65 = all_104_1_56
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (14) with all_1_0_0, all_1_3_3, all_86_3_30, all_104_1_56 and discharging atoms apart_point_and_line(all_1_0_0, all_1_3_3) = all_104_1_56, apart_point_and_line(all_1_0_0, all_1_3_3) = all_86_3_30, yields:
% 24.28/6.42 | (553) all_104_1_56 = all_86_3_30
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (11) with all_1_2_2, all_1_3_3, all_102_2_54, all_104_2_57 and discharging atoms convergent_lines(all_1_2_2, all_1_3_3) = all_104_2_57, convergent_lines(all_1_2_2, all_1_3_3) = all_102_2_54, yields:
% 24.28/6.42 | (554) all_104_2_57 = all_102_2_54
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (11) with all_1_2_2, all_1_3_3, all_100_2_51, all_104_2_57 and discharging atoms convergent_lines(all_1_2_2, all_1_3_3) = all_104_2_57, convergent_lines(all_1_2_2, all_1_3_3) = all_100_2_51, yields:
% 24.28/6.42 | (555) all_104_2_57 = all_100_2_51
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (11) with all_1_2_2, all_1_3_3, all_92_2_39, all_104_2_57 and discharging atoms convergent_lines(all_1_2_2, all_1_3_3) = all_104_2_57, convergent_lines(all_1_2_2, all_1_3_3) = all_92_2_39, yields:
% 24.28/6.42 | (556) all_104_2_57 = all_92_2_39
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (27) with all_1_0_0 yields:
% 24.28/6.42 | (557) ~ (distinct_points(all_1_0_0, all_1_0_0) = 0)
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_0_0, all_1_0_0, all_100_0_49, all_104_0_55 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_104_0_55, distinct_points(all_1_0_0, all_1_0_0) = all_100_0_49, yields:
% 24.28/6.42 | (558) all_104_0_55 = all_100_0_49
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_0_0, all_1_0_0, all_98_0_46, all_104_0_55 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_104_0_55, distinct_points(all_1_0_0, all_1_0_0) = all_98_0_46, yields:
% 24.28/6.42 | (559) all_104_0_55 = all_98_0_46
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_0_0, all_1_0_0, all_94_0_40, all_98_0_46 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_98_0_46, distinct_points(all_1_0_0, all_1_0_0) = all_94_0_40, yields:
% 24.28/6.42 | (560) all_98_0_46 = all_94_0_40
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_0_0, all_1_0_0, all_90_0_34, all_94_0_40 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_94_0_40, distinct_points(all_1_0_0, all_1_0_0) = all_90_0_34, yields:
% 24.28/6.42 | (561) all_94_0_40 = all_90_0_34
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_0_0, all_1_0_0, all_88_0_31, all_104_0_55 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_104_0_55, distinct_points(all_1_0_0, all_1_0_0) = all_88_0_31, yields:
% 24.28/6.42 | (562) all_104_0_55 = all_88_0_31
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_1_1, all_1_0_0, all_102_0_52, 0 and discharging atoms distinct_points(all_1_1_1, all_1_0_0) = all_102_0_52, distinct_points(all_1_1_1, all_1_0_0) = 0, yields:
% 24.28/6.42 | (563) all_102_0_52 = 0
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_1_1, all_1_0_0, all_92_0_37, all_102_0_52 and discharging atoms distinct_points(all_1_1_1, all_1_0_0) = all_102_0_52, distinct_points(all_1_1_1, all_1_0_0) = all_92_0_37, yields:
% 24.28/6.42 | (564) all_102_0_52 = all_92_0_37
% 24.28/6.42 |
% 24.28/6.42 | Instantiating formula (5) with all_1_1_1, all_1_0_0, all_88_2_33, all_92_0_37 and discharging atoms distinct_points(all_1_1_1, all_1_0_0) = all_92_0_37, distinct_points(all_1_1_1, all_1_0_0) = all_88_2_33, yields:
% 24.28/6.42 | (565) all_92_0_37 = all_88_2_33
% 24.28/6.42 |
% 24.28/6.42 | Combining equations (545,551) yields a new equation:
% 24.28/6.42 | (566) all_350_0_155 = all_120_1_66
% 24.28/6.42 |
% 24.28/6.42 | Simplifying 566 yields:
% 24.28/6.42 | (567) all_350_0_155 = all_120_1_66
% 24.28/6.42 |
% 24.28/6.42 | Combining equations (546,567) yields a new equation:
% 24.28/6.42 | (568) all_340_1_149 = all_120_1_66
% 24.28/6.42 |
% 24.28/6.42 | Simplifying 568 yields:
% 24.28/6.42 | (569) all_340_1_149 = all_120_1_66
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (538,543) yields a new equation:
% 24.28/6.43 | (570) all_335_0_145 = all_255_1_88
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 570 yields:
% 24.28/6.43 | (571) all_335_0_145 = all_255_1_88
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (547,569) yields a new equation:
% 24.28/6.43 | (572) all_255_0_87 = all_120_1_66
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 572 yields:
% 24.28/6.43 | (573) all_255_0_87 = all_120_1_66
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (540,571) yields a new equation:
% 24.28/6.43 | (574) all_285_0_109 = all_255_1_88
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 574 yields:
% 24.28/6.43 | (575) all_285_0_109 = all_255_1_88
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (541,539) yields a new equation:
% 24.28/6.43 | (576) all_285_0_109 = all_58_1_21
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 576 yields:
% 24.28/6.43 | (577) all_285_0_109 = all_58_1_21
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (542,575) yields a new equation:
% 24.28/6.43 | (578) all_275_1_103 = all_255_1_88
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 578 yields:
% 24.28/6.43 | (579) all_275_1_103 = all_255_1_88
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (577,575) yields a new equation:
% 24.28/6.43 | (580) all_255_1_88 = all_58_1_21
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (579,544) yields a new equation:
% 24.28/6.43 | (581) all_255_1_88 = all_88_1_32
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 581 yields:
% 24.28/6.43 | (582) all_255_1_88 = all_88_1_32
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (548,573) yields a new equation:
% 24.28/6.43 | (583) all_250_0_84 = all_120_1_66
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 583 yields:
% 24.28/6.43 | (584) all_250_0_84 = all_120_1_66
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (582,580) yields a new equation:
% 24.28/6.43 | (585) all_88_1_32 = all_58_1_21
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 585 yields:
% 24.28/6.43 | (586) all_88_1_32 = all_58_1_21
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (550,584) yields a new equation:
% 24.28/6.43 | (587) all_120_0_65 = all_120_1_66
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 587 yields:
% 24.28/6.43 | (588) all_120_0_65 = all_120_1_66
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (549,588) yields a new equation:
% 24.28/6.43 | (589) all_120_1_66 = all_32_1_8
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (552,588) yields a new equation:
% 24.28/6.43 | (590) all_120_1_66 = all_104_1_56
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (590,589) yields a new equation:
% 24.28/6.43 | (591) all_104_1_56 = all_32_1_8
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 591 yields:
% 24.28/6.43 | (592) all_104_1_56 = all_32_1_8
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (559,558) yields a new equation:
% 24.28/6.43 | (593) all_100_0_49 = all_98_0_46
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (562,558) yields a new equation:
% 24.28/6.43 | (594) all_100_0_49 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (592,553) yields a new equation:
% 24.28/6.43 | (595) all_86_3_30 = all_32_1_8
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (556,554) yields a new equation:
% 24.28/6.43 | (596) all_102_2_54 = all_92_2_39
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (555,554) yields a new equation:
% 24.28/6.43 | (597) all_102_2_54 = all_100_2_51
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (564,563) yields a new equation:
% 24.28/6.43 | (598) all_92_0_37 = 0
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 598 yields:
% 24.28/6.43 | (599) all_92_0_37 = 0
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (597,596) yields a new equation:
% 24.28/6.43 | (600) all_100_2_51 = all_92_2_39
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 600 yields:
% 24.28/6.43 | (601) all_100_2_51 = all_92_2_39
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (593,594) yields a new equation:
% 24.28/6.43 | (602) all_98_0_46 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 602 yields:
% 24.28/6.43 | (603) all_98_0_46 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (560,603) yields a new equation:
% 24.28/6.43 | (604) all_94_0_40 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 604 yields:
% 24.28/6.43 | (605) all_94_0_40 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (561,605) yields a new equation:
% 24.28/6.43 | (606) all_90_0_34 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 606 yields:
% 24.28/6.43 | (607) all_90_0_34 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (565,599) yields a new equation:
% 24.28/6.43 | (608) all_88_2_33 = 0
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 608 yields:
% 24.28/6.43 | (609) all_88_2_33 = 0
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (596,554) yields a new equation:
% 24.28/6.43 | (556) all_104_2_57 = all_92_2_39
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (595,553) yields a new equation:
% 24.28/6.43 | (592) all_104_1_56 = all_32_1_8
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (594,558) yields a new equation:
% 24.28/6.43 | (562) all_104_0_55 = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | From (601) and (219) follows:
% 24.28/6.43 | (204) convergent_lines(all_1_2_2, all_1_3_3) = all_92_2_39
% 24.28/6.43 |
% 24.28/6.43 | From (607) and (200) follows:
% 24.28/6.43 | (194) distinct_points(all_1_0_0, all_1_0_0) = all_88_0_31
% 24.28/6.43 |
% 24.28/6.43 | Using (194) and (557) yields:
% 24.28/6.43 | (615) ~ (all_88_0_31 = 0)
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (196), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (616) ~ (all_88_1_32 = 0)
% 24.28/6.43 |
% 24.28/6.43 | Equations (586) can reduce 616 to:
% 24.28/6.43 | (617) ~ (all_58_1_21 = 0)
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (142), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (618) all_58_1_21 = 0
% 24.28/6.43 |
% 24.28/6.43 | Equations (618) can reduce 617 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.43 | (617) ~ (all_58_1_21 = 0)
% 24.28/6.43 | (621) all_47_0_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & distinct_lines(all_47_1_15, all_17_2_6) = v1 & distinct_points(all_1_0_0, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (621), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (232) all_47_0_14 = 0
% 24.28/6.43 |
% 24.28/6.43 | Equations (232) can reduce 135 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.43 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.43 | (625) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v2 & apart_point_and_line(all_1_1_1, all_17_2_6) = v3 & distinct_lines(all_47_1_15, all_17_2_6) = v1 & distinct_points(all_1_0_0, all_1_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.43 |
% 24.28/6.43 | Instantiating formula (41) with all_92_2_39, all_1_3_3, all_1_2_2, all_1_3_3 and discharging atoms convergent_lines(all_1_2_2, all_1_3_3) = all_92_2_39, convergent_lines(all_1_3_3, all_1_2_2) = 0, ~ (convergent_lines(all_1_3_3, all_1_3_3) = 0), yields:
% 24.28/6.43 | (626) all_92_2_39 = 0
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (626,556) yields a new equation:
% 24.28/6.43 | (627) all_104_2_57 = 0
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (231), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (628) ~ (all_104_2_57 = 0)
% 24.28/6.43 |
% 24.28/6.43 | Equations (627) can reduce 628 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.43 | (627) all_104_2_57 = 0
% 24.28/6.43 | (631) all_104_0_55 = 0 | ( ~ (all_104_1_56 = 0) & ~ (all_32_0_7 = 0))
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (631), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (632) all_104_0_55 = 0
% 24.28/6.43 |
% 24.28/6.43 | Combining equations (562,632) yields a new equation:
% 24.28/6.43 | (633) all_88_0_31 = 0
% 24.28/6.43 |
% 24.28/6.43 | Simplifying 633 yields:
% 24.28/6.43 | (634) all_88_0_31 = 0
% 24.28/6.43 |
% 24.28/6.43 | Equations (634) can reduce 615 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.43 | (636) ~ (all_104_0_55 = 0)
% 24.28/6.43 | (637) ~ (all_104_1_56 = 0) & ~ (all_32_0_7 = 0)
% 24.28/6.43 |
% 24.28/6.43 | Applying alpha-rule on (637) yields:
% 24.28/6.43 | (638) ~ (all_104_1_56 = 0)
% 24.28/6.43 | (639) ~ (all_32_0_7 = 0)
% 24.28/6.43 |
% 24.28/6.43 | Equations (592) can reduce 638 to:
% 24.28/6.43 | (640) ~ (all_32_1_8 = 0)
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (73), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (641) all_32_0_7 = 0
% 24.28/6.43 |
% 24.28/6.43 | Equations (641) can reduce 639 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.43 | (639) ~ (all_32_0_7 = 0)
% 24.28/6.43 | (644) all_32_1_8 = 0 | all_32_2_9 = 0 | all_32_3_10 = 0
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (143), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (232) all_47_0_14 = 0
% 24.28/6.43 |
% 24.28/6.43 | Equations (232) can reduce 135 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.43 | (135) ~ (all_47_0_14 = 0)
% 24.28/6.43 | (648) all_32_1_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (648), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (649) all_32_1_8 = 0
% 24.28/6.43 |
% 24.28/6.43 | Equations (649) can reduce 640 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.43 | (640) ~ (all_32_1_8 = 0)
% 24.28/6.43 | (652) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_47_1_15) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_47_1_15, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 24.28/6.43 |
% 24.28/6.43 +-Applying beta-rule and splitting (644), into two cases.
% 24.28/6.43 |-Branch one:
% 24.28/6.43 | (649) all_32_1_8 = 0
% 24.28/6.43 |
% 24.28/6.43 | Equations (649) can reduce 640 to:
% 24.28/6.43 | (77) $false
% 24.28/6.43 |
% 24.28/6.43 |-The branch is then unsatisfiable
% 24.28/6.43 |-Branch two:
% 24.28/6.44 | (640) ~ (all_32_1_8 = 0)
% 24.28/6.44 | (656) all_32_2_9 = 0 | all_32_3_10 = 0
% 24.28/6.44 |
% 24.28/6.44 +-Applying beta-rule and splitting (656), into two cases.
% 24.28/6.44 |-Branch one:
% 24.28/6.44 | (253) all_32_2_9 = 0
% 24.28/6.44 |
% 24.28/6.44 | Equations (253) can reduce 133 to:
% 24.28/6.44 | (77) $false
% 24.28/6.44 |
% 24.28/6.44 |-The branch is then unsatisfiable
% 24.28/6.44 |-Branch two:
% 24.28/6.44 | (133) ~ (all_32_2_9 = 0)
% 24.28/6.44 | (240) all_32_3_10 = 0
% 24.28/6.44 |
% 24.28/6.44 | Equations (240) can reduce 134 to:
% 24.28/6.44 | (77) $false
% 24.28/6.44 |
% 24.28/6.44 |-The branch is then unsatisfiable
% 24.28/6.44 |-Branch two:
% 24.28/6.44 | (662) all_88_1_32 = 0
% 24.28/6.44 | (663) ~ (all_88_2_33 = 0) | all_88_0_31 = 0
% 24.28/6.44 |
% 24.28/6.44 +-Applying beta-rule and splitting (663), into two cases.
% 24.28/6.44 |-Branch one:
% 24.28/6.44 | (664) ~ (all_88_2_33 = 0)
% 24.28/6.44 |
% 24.28/6.44 | Equations (609) can reduce 664 to:
% 24.28/6.44 | (77) $false
% 24.28/6.44 |
% 24.28/6.44 |-The branch is then unsatisfiable
% 24.28/6.44 |-Branch two:
% 24.28/6.44 | (609) all_88_2_33 = 0
% 24.28/6.44 | (634) all_88_0_31 = 0
% 24.28/6.44 |
% 24.28/6.44 | Equations (634) can reduce 615 to:
% 24.28/6.44 | (77) $false
% 24.28/6.44 |
% 24.28/6.44 |-The branch is then unsatisfiable
% 24.28/6.44 |-Branch two:
% 24.28/6.44 | (232) all_47_0_14 = 0
% 24.28/6.44 | (670) ~ (all_47_2_16 = 0)
% 24.28/6.44 |
% 24.28/6.44 | Equations (119) can reduce 670 to:
% 24.28/6.44 | (77) $false
% 24.28/6.44 |
% 24.28/6.44 |-The branch is then unsatisfiable
% 24.28/6.44 |-Branch two:
% 24.28/6.44 | (672) ~ (distinct_points(all_1_0_0, all_1_1_1) = 0)
% 24.28/6.44 | (76) all_17_0_4 = 0
% 24.28/6.44 |
% 24.28/6.44 | Equations (76) can reduce 61 to:
% 24.28/6.44 | (77) $false
% 24.28/6.44 |
% 24.28/6.44 |-The branch is then unsatisfiable
% 24.28/6.44 |-Branch two:
% 24.28/6.44 | (94) all_17_1_5 = 0
% 24.28/6.44 | (76) all_17_0_4 = 0
% 24.28/6.44 |
% 24.28/6.44 | Equations (76) can reduce 61 to:
% 24.28/6.44 | (77) $false
% 24.28/6.44 |
% 24.28/6.44 |-The branch is then unsatisfiable
% 24.28/6.44 % SZS output end Proof for theBenchmark
% 24.28/6.44
% 24.28/6.44 5814ms
%------------------------------------------------------------------------------